Title of Lesson: Patterns and Inductive Reasoning Section: 1.1Pages: 3-9.

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Presentation transcript:

Title of Lesson: Patterns and Inductive Reasoning Section: 1.1Pages: 3-9

My Learning Goals 1.Find pattern and be able to justify the logic. 2. Use inductive reasoning to make conjectures. 3. State counterexamples to prove conjectures false.

Vocabulary/Formulas 1. Inductive Reasoning: Looking for patterns and making conjectures. 2. Conjecture: An unproven statement based on observations 3. Counterexample: An example that proves a conjecture false

Prerequisite Skills with Practice 1.Evaluate:2.Approximate the square root without a calculator:

Notes Finding pattern based on observations. Mobius Strip Activity.

Notes Text: Inductive Reasoning- 1.Look for a pattern 2.Make a conjecture 3. Verify the conjecture Problem If this pattern continues, how many squares will be in the ninth figure?

Notes Text: More inductive reasoning Problem How many suns in the eighth figure?

Notes Text: More inductive reasoning Problem: How many moons in the tenth figure?

Notes Text: Counterexamples prove conjectures wrong. Only a single counterexample is needed to debunk a conjecture. Problem: Conjecture – “All prime numbers are odd.” Counterexample - Conjecture – “All birds can fly.” Counterexample -

Notes Text: More counterexamples Problem Conjecture – “The square root of x is always less that x. Conjecture – All dinosaurs were green.

Homework Assignment: Page 6 (1-10 all) (17-28) all (34-37) all